Bereken voor je eigen reeks de centrummaten

R Software Module: rwasp_centraltendency.wasp (opens new window with default values)

Title produced by software: Central Tendency

Date of computation: Thu, 17 Apr 2008 12:21:43 -0600

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2008/Apr/17/t1208456580ddsmtujx6qu41ah.htm/, Retrieved Thu, 17 Apr 2008 20:23:00 +0200

User-defined keywords:

Dataseries X:

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105,18 105,18 105,18 105,18 105,18 105,18 105,18 105,18 105,18 105,18 97,82 97,83 97,82 97,83 97,82 97,82 97,8 97,8 97,44 97,44 97,44 97,44 97,7 97,7 97,7 97,7 97,7 97,7 97,7 97,7 97,7 97,7 97,7 89,38 89,38 89,38 89,38 87,69 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 89,21 92,07 92,07 92,07 92,07 92,07 92,07 92,07 92,07 92,07 92,07 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94 94

Text written by user:

Output produced by software:

Summary of compuational transaction Raw Input view raw input (R code) Raw Output view raw output of R engine Computing time 3 seconds R Server 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 Central Tendency - Ungrouped Data Measure Value S.E. Value/S.E. Arithmetic Mean 93.9940625 0.519476617048965 180.939929565955 Geometric Mean 93.8615588946257 Harmonic Mean 93.7328792001276 Quadratic Mean 94.130335710873 Winsorized Mean ( 1 / 32 ) 94.0098958333333 0.51769227919529 181.594162423021 Winsorized Mean ( 2 / 32 ) 94.0098958333333 0.51769227919529 181.594162423021 Winsorized Mean ( 3 / 32 ) 94.0098958333333 0.51769227919529 181.594162423021 Winsorized Mean ( 4 / 32 ) 94.0098958333333 0.51769227919529 181.594162423021 Winsorized Mean ( 5 / 32 ) 94.0098958333333 0.51769227919529 181.594162423021 Winsorized Mean ( 6 / 32 ) 94.0098958333333 0.51769227919529 181.594162423021 Winsorized Mean ( 7 / 32 ) 94.0098958333333 0.51769227919529 181.594162423021 Winsorized Mean ( 8 / 32 ) 94.0098958333333 0.51769227919529 181.594162423021 Winsorized Mean ( 9 / 32 ) 94.0098958333333 0.51769227919529 181.594162423021 Winsorized Mean ( 10 / 32 ) 93.2442708333333 0.375533910702531 248.297871845704 Winsorized Mean ( 11 / 32 ) 93.2442708333333 0.375533910702531 248.297871845704 Winsorized Mean ( 12 / 32 ) 93.2430208333333 0.375373355655116 248.400744028840 Winsorized Mean ( 13 / 32 ) 93.2430208333333 0.375373355655116 248.400744028840 Winsorized Mean ( 14 / 32 ) 93.2430208333333 0.375373355655116 248.400744028840 Winsorized Mean ( 15 / 32 ) 93.2430208333333 0.375373355655116 248.400744028840 Winsorized Mean ( 16 / 32 ) 93.2396875 0.374946062001771 248.674934741839 Winsorized Mean ( 17 / 32 ) 93.2396875 0.374946062001771 248.674934741839 Winsorized Mean ( 18 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 19 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 20 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 21 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 22 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 23 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 24 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 25 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 26 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 27 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 28 / 32 ) 93.2209375 0.372559340561452 250.217689776654 Winsorized Mean ( 29 / 32 ) 93.1423958333333 0.362690383907217 256.809664568225 Winsorized Mean ( 30 / 32 ) 93.1423958333333 0.362690383907217 256.809664568225 Winsorized Mean ( 31 / 32 ) 93.1423958333333 0.362690383907217 256.809664568225 Winsorized Mean ( 32 / 32 ) 93.1423958333333 0.362690383907217 256.809664568225 Trimmed Mean ( 1 / 32 ) 93.9421276595745 0.51248051834432 183.308680616924 Trimmed Mean ( 2 / 32 ) 93.8714130434783 0.50638818255984 185.374414878620 Trimmed Mean ( 3 / 32 ) 93.7975555555555 0.499277838310487 187.866451018452 Trimmed Mean ( 4 / 32 ) 93.720340909091 0.490983127804303 190.883017361945 Trimmed Mean ( 5 / 32 ) 93.639534883721 0.481300219920655 194.555354450405 Trimmed Mean ( 6 / 32 ) 93.554880952381 0.46997572275429 199.063220551272 Trimmed Mean ( 7 / 32 ) 93.4660975609756 0.45668904382424 204.660258057223 Trimmed Mean ( 8 / 32 ) 93.372875 0.441025638400157 211.717566667359 Trimmed Mean ( 9 / 32 ) 93.2748717948718 0.422434461085282 220.803178687738 Trimmed Mean ( 10 / 32 ) 93.1717105263158 0.400156083063294 232.838420980791 Trimmed Mean ( 11 / 32 ) 93.1622972972973 0.402535123935019 231.438927332802 Trimmed Mean ( 12 / 32 ) 93.1523611111111 0.404854950602327 230.088235237145 Trimmed Mean ( 13 / 32 ) 93.142 0.407120555852845 228.782356137444 Trimmed Mean ( 14 / 32 ) 93.1310294117647 0.409288078656553 227.543958078276 Trimmed Mean ( 15 / 32 ) 93.119393939394 0.411330315417816 226.385925007269 Trimmed Mean ( 16 / 32 ) 93.10703125 0.413214129297591 225.32392928642 Trimmed Mean ( 17 / 32 ) 93.0941935483871 0.414959081172398 224.345478318886 Trimmed Mean ( 18 / 32 ) 93.0805 0.41646334643826 223.502262074339 Trimmed Mean ( 19 / 32 ) 93.0675862068966 0.418005759413544 222.6466600304 Trimmed Mean ( 20 / 32 ) 93.05375 0.419222576912917 221.96741092818 Trimmed Mean ( 21 / 32 ) 93.0388888888889 0.420029837104186 221.505428115125 Trimmed Mean ( 22 / 32 ) 93.0228846153846 0.420321317918826 221.313744151682 Trimmed Mean ( 23 / 32 ) 93.0056 0.419961335440903 221.462292242586 Trimmed Mean ( 24 / 32 ) 92.986875 0.418774613572167 222.045157434013 Trimmed Mean ( 25 / 32 ) 92.9665217391304 0.416531713494887 223.191941278852 Trimmed Mean ( 26 / 32 ) 92.9443181818182 0.412927515373029 225.086279604919 Trimmed Mean ( 27 / 32 ) 92.92 0.407548405310722 227.997456962581 Trimmed Mean ( 28 / 32 ) 92.89325 0.399820214003296 232.337552596163 Trimmed Mean ( 29 / 32 ) 92.8636842105263 0.388921333752945 238.772410128358 Trimmed Mean ( 30 / 32 ) 92.8380555555556 0.376234016049123 246.756145365214 Trimmed Mean ( 31 / 32 ) 92.8094117647059 0.358232674460419 259.07578616188 Trimmed Mean ( 32 / 32 ) 92.7771875 0.332323878402155 279.177012335321 Median 94 Midrange 96.435 Midmean - Weighted Average at Xnp 92.225974025974 Midmean - Weighted Average at X(n+1)p 92.225974025974 Midmean - Empirical Distribution Function 92.225974025974 Midmean - Empirical Distribution Function - Averaging 92.225974025974 Midmean - Empirical Distribution Function - Interpolation 92.225974025974 Midmean - Closest Observation 92.225974025974 Midmean - True Basic - Statistics Graphics Toolkit 92.225974025974 Midmean - MS Excel (old versions) 92.225974025974 Number of observations 96

Charts produced by software:

http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208456580ddsmtujx6qu41ah/180ev1208456498.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208456580ddsmtujx6qu41ah/180ev1208456498.ps (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208456580ddsmtujx6qu41ah/2qtp01208456498.png (open in new window) http://127.0.0.1/wessadotnet/public_html/freestatisticsdotorg/blog/date/2008/Apr/17/t1208456580ddsmtujx6qu41ah/2qtp01208456498.ps (open in new window)

Parameters (Session):

Parameters (R input):

R code (references can be found in the software module):

geomean <- function(x) { return(exp(mean(log(x)))) } harmean <- function(x) { return(1/mean(1/x)) } quamean <- function(x) { return(sqrt(mean(x*x))) } winmean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) win <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn } return(win) } trimean <- function(x) { x <-sort(x[!is.na(x)]) n<-length(x) denom <- 3 nodenom <- n/denom if (nodenom>40) denom <- n/40 sqrtn = sqrt(n) roundnodenom = floor(nodenom) tri <- array(NA,dim=c(roundnodenom,2)) for (j in 1:roundnodenom) { tri[j,1] <- mean(x,trim=j/n) tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2) } return(tri) } midrange <- function(x) { return((max(x)+min(x))/2) } q1 <- function(data,n,p,i,f) { np <- n*p; i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q2 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i qvalue <- (1-f)*data[i] + f*data[i+1] } q3 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- data[i+1] } } q4 <- function(data,n,p,i,f) { np <- n*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- (data[i]+data[i+1])/2 } else { qvalue <- data[i+1] } } q5 <- function(data,n,p,i,f) { np <- (n-1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i+1] } else { qvalue <- data[i+1] + f*(data[i+2]-data[i+1]) } } q6 <- function(data,n,p,i,f) { np <- n*p+0.5 i <<- floor(np) f <<- np - i qvalue <- data[i] } q7 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { qvalue <- f*data[i] + (1-f)*data[i+1] } } q8 <- function(data,n,p,i,f) { np <- (n+1)*p i <<- floor(np) f <<- np - i if (f==0) { qvalue <- data[i] } else { if (f == 0.5) { qvalue <- (data[i]+data[i+1])/2 } else { if (f < 0.5) { qvalue <- data[i] } else { qvalue <- data[i+1] } } } } midmean <- function(x,def) { x <-sort(x[!is.na(x)]) n<-length(x) if (def==1) { qvalue1 <- q1(x,n,0.25,i,f) qvalue3 <- q1(x,n,0.75,i,f) } if (def==2) { qvalue1 <- q2(x,n,0.25,i,f) qvalue3 <- q2(x,n,0.75,i,f) } if (def==3) { qvalue1 <- q3(x,n,0.25,i,f) qvalue3 <- q3(x,n,0.75,i,f) } if (def==4) { qvalue1 <- q4(x,n,0.25,i,f) qvalue3 <- q4(x,n,0.75,i,f) } if (def==5) { qvalue1 <- q5(x,n,0.25,i,f) qvalue3 <- q5(x,n,0.75,i,f) } if (def==6) { qvalue1 <- q6(x,n,0.25,i,f) qvalue3 <- q6(x,n,0.75,i,f) } if (def==7) { qvalue1 <- q7(x,n,0.25,i,f) qvalue3 <- q7(x,n,0.75,i,f) } if (def==8) { qvalue1 <- q8(x,n,0.25,i,f) qvalue3 <- q8(x,n,0.75,i,f) } midm <- 0 myn <- 0 roundno4 <- round(n/4) round3no4 <- round(3*n/4) for (i in 1:n) { if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){ midm = midm + x[i] myn = myn + 1 } } midm = midm / myn return(midm) } (arm <- mean(x)) sqrtn <- sqrt(length(x)) (armse <- sd(x) / sqrtn) (armose <- arm / armse) (geo <- geomean(x)) (har <- harmean(x)) (qua <- quamean(x)) (win <- winmean(x)) (tri <- trimean(x)) (midr <- midrange(x)) midm <- array(NA,dim=8) for (j in 1:8) midm[j] <- midmean(x,j) midm bitmap(file='test1.png') lb <- win[,1] - 2*win[,2] ub <- win[,1] + 2*win[,2] if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() bitmap(file='test2.png') lb <- tri[,1] - 2*tri[,2] ub <- tri[,1] + 2*tri[,2] if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax)) lines(ub,lty=3) lines(lb,lty=3) grid() dev.off() load(file='createtable') a<-table.start() a<-table.row.start(a) a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Measure',header=TRUE) a<-table.element(a,'Value',header=TRUE) a<-table.element(a,'S.E.',header=TRUE) a<-table.element(a,'Value/S.E.',header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE) a<-table.element(a,arm) a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean')) a<-table.element(a,armose) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE) a<-table.element(a,geo) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE) a<-table.element(a,har) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE) a<-table.element(a,qua) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) for (j in 1:length(win[,1])) { a<-table.row.start(a) mylabel <- paste('Winsorized Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(win[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE) a<-table.element(a,win[j,1]) a<-table.element(a,win[j,2]) a<-table.element(a,win[j,1]/win[j,2]) a<-table.row.end(a) } for (j in 1:length(tri[,1])) { a<-table.row.start(a) mylabel <- paste('Trimmed Mean (',j) mylabel <- paste(mylabel,'/') mylabel <- paste(mylabel,length(tri[,1])) mylabel <- paste(mylabel,')') a<-table.element(a,hyperlink('http://www.xycoon.com/arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE) a<-table.element(a,tri[j,1]) a<-table.element(a,tri[j,2]) a<-table.element(a,tri[j,1]/tri[j,2]) a<-table.row.end(a) } a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE) a<-table.element(a,median(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,hyperlink('http://www.xycoon.com/midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE) a<-table.element(a,midr) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_1.htm','Weighted Average at Xnp',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[1]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[2]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_3.htm','Empirical Distribution Function',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[3]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[4]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[5]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_6.htm','Closest Observation',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[6]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[7]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) mymid <- hyperlink('http://www.xycoon.com/midmean.htm', 'Midmean', 'click to view the definition of the Midmean') mylabel <- paste(mymid,hyperlink('http://www.xycoon.com/method_8.htm','MS Excel (old versions)',''),sep=' - ') a<-table.element(a,mylabel,header=TRUE) a<-table.element(a,midm[8]) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,'Number of observations',header=TRUE) a<-table.element(a,length(x)) a<-table.element(a,'') a<-table.element(a,'') a<-table.row.end(a) a<-table.end(a) table.save(a,file='mytable.tab')

Copyright

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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